Problem

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Tags: geometry, emc



Two circles C1 and C2 intersect at points A and B. Let P, Q be points on circles C1, C2 respectively, such that |AP|=|AQ|. The segment PQ intersects circles C1 and C2 in points M, N respectively. Let C be the center of the arc BP of C1 which does not contain point A and let D be the center of arc BQ of C2 which does not contain point A Let E be the intersection of CM and DN. Prove that AE is perpendicular to CD. Proposed by Steve Dinh